Extending binary operations to funtor-spaces

Abstract

Given a continuous monadic functor T : Comp → Comp in the category of compacta and a discrete topological semigroup X we extend the semigroup operation ϕ : X × X → X to a right-topological semigroup operation Φ : T βX × T βX → T βX whose topological center ΛΦ contains the dense subsemigroup T f X consisting of elements a ∈ T βX that have finite support in X.